Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters

In this paper we implement a combination of data-science and fuzzy theory to improve the classical Barndorff-Nielsen and Shephard model, and implement this to analyze the S&P 500 index. We preprocess the index data based on fuzzy theory. After that, S&P 500 stock index data for the past 10 years are analyzed, and a deterministic parameter is extracted using various machine and deep learning methods. The results show that the new model, where fuzzy parameters are incorporated, can incorporate the long-term dependence in the classical Barndorff-Nielsen and Shephard model. The modification is based on only a few changes compared to the classical model. At the same time, the resulting analysis effectively captures the stochastic dynamics of the stock index time series.